A primer on noise-induced transitions in applied dynamical systems

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Abstract

Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in large behavioral changes such as transitions between or escapes from quasi-stable states. These transitions can correspond to critical events such as failures or extinctions that make them essential phenomena to understand and quantify, despite the fact that their occurrence is rare. This article will provide an overview of the theory underlying the dynamics of rare events for stochastic models along with some example applications.

Original languageEnglish
Pages (from-to)969-1009
Number of pages41
JournalSIAM Review
Volume60
Issue number4
DOIs
StatePublished - Jan 1 2018

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Theoretical Computer Science
  • Applied Mathematics

Keywords

  • Bit error ratios
  • Dynamical systems
  • Epidemiology
  • Escape
  • Extinction
  • Large deviation theory
  • Mean exit time
  • Mode-locked lasers
  • Noise-induced transitions
  • Optimal path
  • Rare events
  • Stochasticity

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